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of a video stream, quantization error and truncation error are introduced. These
errors are lossy and thus cannot be removed from the decompressed data. In order
to reduce the noise signals, we decided to apply a FIR low-pass filter (LPF) to
the frame distance function. Low-pass filtering is implemented by using a sliding
window of length
L
, and the average of the frame distance values in the sliding
window is used to replace the current frame distance. The low-pass filtering function
is as follows:
L
1
j
=
0
D
(
n
−
j
)
−
1
L
F
(
D
(
n
)
,
L
)=
(7.3)
Although the quantized value should be rounded to the nearest integer during
quantization, it is common practice to round it down to increase the compression
ratio. MPEG has two default quantization matrices for intra-frames and non-intra
frames, and it also supports user defined quantization matrices. Depending on the
quantization matrix used and the bin size of the energy histogram, the de-quantized
DC coefficients of a data block can be shifted to a different energy range, leading to
noise in the frame distance function. By using a sliding window, this noise signal is
reduced and becomes less significant.
Floating point calculation is performed during MPEG compression and the pro-
cess of obtaining DC coefficients from P-frames. This truncation error accumulates
until the next I-frame is encountered, and thus it resembles a triangular signal. This
noise signal tends to peak when the current frame is an I-frame, and it is the least
significant when the previous frame is an I-frame. For a pure triangular signal with a
period of
T
, it can be reduced to a DC signal by using a sliding window of length
T
.
Since there is usually one I-frame in a group of pictures (GOP), we set the length of
the filter
L
to be equal to the total number of I- and P-frames in a GOP. By using a
LPF, the noise signal caused by truncation error is attenuated.
MPEG achieves a high compression ratio by taking advantage of temporal redun-
dancy. In a GOP, I- and P-frames are used as references in motion compensation.
Therefore, it is reasonable to assume that the contents of I- and P-frames in the same
GOP are similar, except when there is a scene change present. For a MPEG video
with a frame rate of 29.97 fps and GOPs of length 15, the duration of a GOP is
only 0.5 s. In this case, the contents of adjacent GOPs are highly correlated, and the
average frame distances of the two GOP are similar in magnitude. That is, the ratio
between the two average frame distances has a value close to 1. Since the presence
of a transition is indicated by an increase in frame distance, this ratio would have a
value larger than 1 when there is a transition in the current GOP. As transitions could
involve more than one GOP, it is more appropriate to consider the ratio between two
sliding windows instead of two actual GOPs. This leads to the TWAM:
D
TWAM
(
n
)=
A
(
D
(
n
)
,
L
1
)
∗
F
(
D
(
n
)
,
L
2
)
(7.4)
L
1
−
1
j
=
0
2
L
1
−
1
∑
j
=
L
1
L
2
−
1
j
=
0
1
L
2
=
D
(
n
−
j
)
D
(
n
−
j
)
∗
D
(
n
−
j
)
(7.5)
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